Mathematical Logic

A comprehensive and user-friendly guide to the use of logic in
mathematical reasoning

Mathematical Logic presents a comprehensive introduction
to formal methods of logic and their use as a reliable tool for
deductive reasoning. With its user-friendly approach, this book
successfully equips readers with the key concepts and methods for
formulating valid mathematical arguments that can be used to
uncover truths across diverse areas of study such as mathematics,
computer science, and philosophy.

The book develops the logical tools for writing proofs by
guiding readers through both the established "Hilbert" style of
proof writing, as well as the "equational" style that is emerging
in computer science and engineering applications. Chapters have
been organized into the two topical areas of Boolean logic and
predicate logic. Techniques situated outside formal logic are
applied to illustrate and demonstrate significant facts regarding
the power and limitations of logic, such as:

Logic can certify truths and only truths.

Logic can certify all absolute truths (completeness theorems of
Post and Gödel).

Logic cannot certify all "conditional" truths, such as those
that are specific to the Peano arithmetic. Therefore, logic has
some serious limitations, as shown through Gödel's
incompleteness theorem.

Numerous examples and problem sets are provided throughout the
text, further facilitating readers' understanding of the
capabilities of logic to discover mathematical truths. In addition,
an extensive appendix introduces Tarski semantics and proceeds with
detailed proofs of completeness and first incompleteness theorems,
while also providing a self-contained introduction to the theory of
computability.

With its thorough scope of coverage and accessible style,
Mathematical Logic is an ideal book for courses in
mathematics, computer science, and philosophy at the
upper-undergraduate and graduate levels. It is also a valuable
reference for researchers and practitioners who wish to learn how
to use logic in their everyday work.

GEORGE TOURLAKIS, PhD, is University Professor of Computer Science and Engineering at York University, Canada. Dr. Tourlakis has authored or coauthored numerous articles in his areas of research interest, which include calculational logic, modal logic, computability, complexity theory, and arithmetical forcing.

“Overall, he presents the material as if he were holding a
dialogue with the reader. An advanced independent reader with a
very strong background in mathematics would find the book helpful
in learning this area of mathematics. Summing Up:
Recommended.” (Choice, April 2009)

"The book would be ideas as an introduction to classical logic
for students of mathematics, computer science or philosophy.
Due to the author's clear and approachable style, it can be
recommended to a large circle of readers interested in mathematical
logic as well." (Mathematical Review, Issue 2009e)

"I give this outstanding book my highest recommendation, whilst
being grateful that excellence in the logic-book 'business' is the
very opposite of a zero-sum game: there's plenty of room at the
top." (Computing Reviews, November 5, 2008)

"The book would be ideas as an introduction to classical logic for
students of mathematics, computer science or philosophy. Due
to the author's clear and approachable style, it can be recommended
to a large circle of readers interested in mathematical logic as
well." (Mathematical Review, Issue 2009e)

"I give this outstanding book my highest recommendation, whilst
being grateful that excellence in the logic-book 'business' is the
very opposite of a zero-sum game: there's plenty of room at the
top." (Computing Reviews, Nov 2008)

Digital version available through Wiley Online Library

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